This bound is attained on the first entry of Table REF , which is the minimal representation.
On the other hand, the original Helgason-Johnson upper bound for \(\Vert \nu \Vert \)  is \(\Vert \rho \Vert =\sqrt{\frac{399}{2}}\)  (see [1]}). This improvement greatly reduces the cardinality of \(\Phi \) , which turns out to be 723855.
As put in Remark REF  below, the sharpened Helgason-Johnson bound will continue to be helpful in doing non-unitarity test.
